PaperlayerView exact revision on arXiv

Source-linked AI summary

Aerodynamic Prior-Free Coordinated Trajectory Generation and Tracking Control for a Tail-Sitter UAV

Erchao Rong, Zihao Liu, Junning Liang, Jianguo Wang, Xiao Jie, Haoran Fu, Ziliang Chen, Ximin Lyu

arXiv:2609.11698v1cs.RO

TL;DR

Tail-sitter control is challenged by nonlinear aerodynamics and the dependence of existing methods on airframe-specific aerodynamic identification. The paper combines an analytic ϕ-theory differential-flatness planner with reduced-model nonlinear MPC that estimates aerodynamics online, achieving high-precision tracking across tested flight regimes while retaining limitations at extreme speeds and under unmodeled conditions.

  • Problem

    Nonlinear full-envelope aerodynamics and costly, airframe-specific model identification hinder portable tail-sitter trajectory planning and tracking.

  • Method

    The framework uses a full ϕ-theory differential-flatness mapping for planning and a simplified locally valid nonlinear MPC model with online aerodynamic parameter estimation for tracking.

  • Results

    The framework closely tracks a high-fidelity MPC upper bound in simulation and maintains precise real-world trajectory execution across tested regimes, including peak velocity 13.3 m/s and attitudes up to 48° roll and 78° pitch.

  • Takeaways & Limitations

    The method can be adapted across configurations and used as an initial controller for collecting flight data without airframe-specific aerodynamic priors.

Abstract

from arXiv · show

This paper presents a coordinated trajectory generation and tracking control framework for a tail-sitter unmanned aerial vehicle (UAV), which does not require aerodynamic priors identified for a specific airframe while addressing the challenge of flight control under highly nonlinear aerodynamics across the full flight envelope. The core innovation lies in employing phase-specific aerodynamic modeling strategies for planning and tracking, tailored to their distinct functional characteristics, without requiring airframe-specific aerodynamic priors. Specifically, the phi-theory model under coordinated flight is employed to derive an analytic differential flatness mapping, and a simplified but locally accurate model is established for predictive control to enable real-time aerodynamic parameter estimation. The proposed framework is evaluated extensively through both simulation and challenging real-world flight tests under mild wind conditions, showing high-precision tracking and adaptability across the tested aerodynamic conditions. To the best of our knowledge, this is the first real-world demonstration of accurate trajectory tracking over tested flight regimes spanning the full envelope of a tail-sitter UAV without relying on aerodynamic identification campaigns. The source code of our framework is available at: https://github.com/SYSU-HILAB/AP-PnC.

I. INTRODUCTION

Tail-sitter flight control is difficult because large attitude shifts create strongly varying, nonlinear aerodynamics, while existing high-performance approaches depend on airframe-specific aerodynamic models. The paper introduces an integrated framework combining analytic trajectory generation and adaptive predictive control without costly aerodynamic identification.

  • I. INTRODUCTION: Prior high-performance tail-sitter controllers rely on high-fidelity aerodynamic models, creating portability, hardware, and computational challenges.The paper positions its approach against model-dependent tracking and planning methods whose predictive performance requires advance aerodynamic characterization.
  • I. INTRODUCTION: The framework addresses nonlinear full-envelope control without requiring airframe-specific aerodynamic identification.It targets portability and reduced deployment cost while retaining coordinated trajectory planning and tracking.
  • I. INTRODUCTION: An analytic differential-flatness mapping based on the full ϕ-theory model generates feasible trajectories and reference states without advance aerodynamic characterization.The mapping uses coordinated-flight dynamics and aerodynamic force relations to avoid explicit dynamic integration during planning.
  • I. INTRODUCTION: A nonlinear MPC estimates and adapts to aerodynamic characteristics online, avoiding costly model-identification campaigns during deployment.The controller is designed to replace extensive aerodynamic estimation setups and resource-intensive identification procedures.
  • I. INTRODUCTION: The paper reports sub-meter position RMSE over tested flight regimes without an aerodynamic identification campaign and provides open-source code for further validation.The framework is evaluated through simulation and experiments, with the source code released for community investigation.

B. Kinematics

The vehicle kinematics describe translational and rotational motion using position derivatives, proper acceleration, angular velocity, inertia, and applied moments. Aerodynamic force, thrust, and thrust-moment models are handled differently in planning and tracking.

  • B. Kinematics: Proper acceleration is defined as the acceleration excluding gravity and is produced by thrust and aerodynamic forces.The translational model uses proper acceleration to connect vehicle motion with force generation.
  • B. Kinematics: The rotational dynamics use the aircraft inertia matrix, body-frame angular velocity, and total moment from aerodynamic and thrust moments.The cross-product operator represents vector products in the rotational equations.
  • B. Kinematics: The nominal system state is defined before separating aerodynamic-force, thrust, and thrust-moment modeling across planning and tracking.Aerodynamic moment is treated as a disturbance and compensated by a low-level controller.

C. System Framework

The framework uses phase-specific aerodynamic models: a feasibility-oriented full-envelope model for long-horizon planning and a locally valid reduced model for short-horizon MPC tracking. It assumes wind-free coordinated flight and estimates a dominant aerodynamic parameter online.

  • C. System Framework: Planning uses differential flatness with the ϕ-theory model, while tracking uses a locally valid simplified model for real-time aerodynamic adaptation.The two models are deliberately tailored to long-horizon trajectory generation and short-horizon predictive control.
  • C. System Framework: The tracking model retains one online-estimated longitudinal aerodynamic parameter while treating other effects through low-level compensation or coordination assumptions.The implementation preserves Bcz, treats Bcx as a matched disturbance, assumes Bcy vanishes under coordination, and neglects aerodynamic moment.
  • C. System Framework: The planner generates a dynamically feasible trajectory offline, extracts position, velocity, and lateral-axis references, and supplies them to online MPC.MPC solves a receding-horizon optimization using augmented state estimates and sends predicted angular velocity and proper acceleration to the low-level controller.
  • C. System Framework: The framework assumes wind-free conditions and coordinated flight, with sustained sideslip maneuvers outside its design scope.Wind is excluded as an aerodynamic disturbance, and lateral-axis tracking is used to suppress sideslip.
  • C. System Framework: Under coordinated flight, differential flatness uses position as the flat output and expresses relevant states and inputs through position derivatives up to third order.The stability-frame kinematic structure and ϕ-theory force relations close the dynamics-dependent portion of the flatness map.

2) ϕ-theory Model:

The ϕ-theory model provides an analytic differential-flatness mapping for coordinated tail-sitter flight, allowing attitude, thrust, and angular velocity references to be derived from position trajectories. Restricting the planning model to ϕ33 enables aerodynamic-prior-free trajectory generation.

  • ϕ-theory Model:: The full-flight-envelope mapping requires an aerodynamic model for angle of attack, obtained by decomposing the dynamics in the longitudinal plane.The longitudinal decomposition relates aerodynamic and proper accelerations through angle of attack.
  • ϕ-theory Model:: The ϕ-theory model avoids generally unavailable closed-form solutions for complex aerodynamic maps by expressing aerodynamic force through ϕ coefficients.Each ϕ coefficient is mass-normalized, and the mass converts modeled aerodynamic acceleration to force.
  • ϕ-theory Model:: ϕ-theory analytically solves angle of attack, enabling computation of attitude and thrust from the modeled aerodynamic force.The resulting body-frame attitude is determined from the rotation between frames, while thrust acceleration is assumed aligned with xb.
  • ϕ-theory Model:: The differential-flatness mapping additionally derives body-frame angular velocity by differentiating the attitude relation and incorporating trajectory jerk.Determining angular velocity requires the time derivative of angle of attack.
  • ϕ-theory Model:: For planning, the model retains only ϕ33 = 0.5ρSCD,flat/m, equivalent to ignoring the axial aerodynamic coefficient Bcx.This restriction defines the aerodynamic prior-free planner using air density, wing area, and flat-plate drag coefficient terms.

B. Spatial-temporal Trajectory Generation

The planner represents trajectories as piecewise seventh-order polynomial splines parameterized by intermediate waypoints and segment times. GCOPTER and TMINCO optimize these variables while enforcing dynamic feasibility through differential-flatness propagation and penalized constraints.

  • B. Spatial-temporal Trajectory Generation: TMINCO parameterizes the trajectory with intermediate waypoints Q and segment durations T, producing piecewise polynomial coefficients.The trajectory contains M segments, with waypoint and time-allocation variables optimized from fixed initial and terminal positions.
  • B. Spatial-temporal Trajectory Generation: Seventh-order polynomial splines provide C3 continuity across the complete trajectory.The polynomial basis is β(s) = (1, s, . . . , s7).
  • B. Spatial-temporal Trajectory Generation: The planner iteratively evaluates TMINCO trajectories, applies differential-flatness propagation, updates variables by line search, and returns the optimized trajectory.The algorithm initializes waypoints and time allocation, uses L-BFGS updates, and terminates when the gradient norm falls below the specified threshold.
  • B. Spatial-temporal Trajectory Generation: GCOPTER converts waypoint, timing, velocity, angular-velocity, and acceleration requirements into an unconstrained nonlinear program.Constraint violations are incorporated into the cost using a quadratic exterior penalty method.
  • B. Spatial-temporal Trajectory Generation: Differential-flatness backpropagation computes constraint gradients along uniformly sampled trajectories and propagates them to waypoint and timing variables.Forward-mode automatic differentiation avoids cumbersome symbolic derivation of the flatness-map gradient.

IV. TRAJECTORY TRACKING CONTROL

The proposed aerodynamic prior-free MPC tracks coordinated-flight trajectories using online aerodynamic-parameter estimation. This enables high-accuracy tracking without requiring airframe-specific aerodynamic characterization in advance.

  • IV. TRAJECTORY TRACKING CONTROL: The aerodynamic prior-free MPC incorporates an online estimated aerodynamic parameter to achieve high-accuracy tracking of coordinated-flight trajectories.The controller is developed under the paper’s phase-specific modeling strategy for tracking control.

A. Prediction Model

The prediction model retains the dominant axial aerodynamic effect while simplifying lateral coefficients and aerodynamic moments. Treating the retained coefficient as a time-varying augmented state enables locally valid adaptive prediction over the full flight envelope.

  • A. Prediction Model: Bcz is augmented into the nominal state and estimated online, allowing adaptive control over the MPC’s short prediction horizon.The parameter is modeled as time-varying because local validity over short horizons is sufficient for MPC.
  • A. Prediction Model: The aerodynamic parameter dynamics encode the typical relation between pitch motion and the magnitude of the axial aerodynamic effect.Pitch down typically decreases its magnitude, whereas pitch up typically increases it.
  • A. Prediction Model: The MPC augments the state with the four actuator thrust forces so generated control force and moment can be constrained.The input is defined through thrust-force rates for the four motors.
  • A. Prediction Model: The retained prediction model is locally valid across the full flight envelope while preserving the most significant aerodynamic effect from the controller’s perspective.This modeling choice supports adaptive tracking without requiring a globally accurate aerodynamic model.

B. MPC Optimization Problem Formulation

The MPC predicts coordinated-flight dynamics while integrating trajectory tracking, control effort, and coordinated-flight costs under actuator and command-bandwidth constraints.

  • The prediction model is effective in coordinated flight but loses validity under significant sideslip, motivating integration with the coordinated-flight strategy.
  • The reference position trajectory and its velocity, acceleration, and body-axis references are obtained from the coordinated-flight planner’s flatness mapping.
  • The MPC softens the coordinated-flight tracking constraint into a cost combining trajectory tracking, control effort, and coordinated-flight terms.
  • Actuator-limit constraints and command-bandwidth tuning enforce dynamical feasibility and controllability of the low-level controller.
  • The continuous-time MPC is transcribed into a nonlinear program and solved in real time using sequential quadratic programming and HPIPM.

C. Augmented State Estimation

The augmented-state estimator focuses on aerodynamic thrust and drag-related components without requiring motor-speed sensing or a pre-identified propeller model.

  • The estimator obtains nominal position, velocity, attitude, and angular-rate states from a standard estimator while focusing on thrust force and aerodynamic parameter components.
  • The thrust force is initialized from the previous MPC result instead of motor-speed measurements, avoiding extra hardware and a pre-identified propeller model.
  • The aerodynamic parameter is estimated from filtered acceleration measurements with a denominator offset and clamping to prevent singularities and over-estimation.

V. EXPERIMENTS

Simulation and field experiments evaluate the aerodynamic prior-free framework across tracking tasks and aggressive transitions, including peak velocity of 13.3 m/s and large roll and pitch angles.

  • The framework maintains precise trajectory execution without aerodynamic priors during aggressive tests reaching 13.3 m/s, 48° roll, and 78° pitch.

A. Benchmark under Various Aerodynamic Conditions

The benchmark compares the proposed controller with prior-based baselines across aerodynamic models and flight regimes, showing near-upper-bound RMSE but larger high-speed worst-case errors and wind-sensitive limits.

  • The experiments use three aerodynamic plants and circular trajectories spanning 8–14 m/s, evaluated by RMSE, MaxAE, and level-flight sideslip angle.
  • The ϕ-theory MPC has MaxAE above 1.5 m under realistic aerodynamic conditions, while cascaded-PID and ϕ-theory MPC show higher tracking errors than the other tested methods.
  • The proposed MPC remains within 0.2 m absolute RMSE of high-fidelity MPC across tested aerodynamic conditions, including 14 m/s.
  • At 14 m/s, relative MaxAE degradation exceeds 100% under Ma et al. and 200% under Lyu et al. conditions.
  • Wind-direction effects shift the vehicle between aerodynamic regimes, with combined headwind and crosswind producing the greatest sensitivity.
  • Figure 5 compares position RMSE, MaxAE, and sideslip across the proposed method, Cascaded-PID, ϕ-theory MPC, and high-fidelity MPC.

C. Field Experiments

Field experiments validate coordinated circular, ∞-shaped, and rapid-transition flights without airframe-specific aerodynamic priors, including aggressive maneuvers and tested wind conditions.

  • Typical Maneuvers in Field Environments: 0.39 m circular-flight position RMSE and 0.42 m ∞-shaped-flight average error demonstrate precise trajectory tracking across three-phase maneuvers.Both trajectories include forward transition, level flight, and backward transition; the circular trajectory reaches 0.66 m MaxAE, while the ∞-shaped trajectory reaches 0.73 m.
  • Typical Maneuvers in Field Environments: The vehicle closely tracks position, velocity, and lateral-axis references despite no aerodynamic priors and maximum tilt exceeding 80°.During level flight, the ground-velocity-based sideslip proxy remains within 10° for nearly the entire duration of both trajectories.
  • Fast Transitions: 0.54 m forward and 0.25 m backward height MaxAE outperform the baseline’s 1.15 m and 1.00 m during the most aggressive transitions.The comparison uses the same low-level controller, while the baseline relies on aerodynamic priors and altitude regulation.
  • Conclusion and Future Work: The framework is presented as adaptable across configurations and suitable for deployment without airframe-specific aerodynamic priors.The authors also describe it as a potential initial controller for collecting flight data for later high-fidelity model-based design.
  • Conclusion and Future Work: Under tested wind disturbances, MaxAE remains at or below 1 m in moderate tailwinds but degrades under mild headwind and crosswind.The worst degradation occurs under combined headwind and crosswind when low-AoA high-stiffness behavior coincides with violation of the coordinated-flight constraint.
Loading 2609.11698v1…